What are the solutions of |3x + 2| > 9?

By using PEDMAS rule, 7 + (5 – 9)2 + 3(16 ÷ 8) is  5.

PEDMAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations. PEMDAS stands for P- Parentheses, E- Exponents, D- Division, M- Multiplication, A- Addition, and S- Subtraction.

Given

7 + (5 – 9)2 + 3(16 ÷ 8)

By using PEDMAS rule,

= 7 + (-4)2 + 3(2)

= 7 + (-8) + 6

= 7 - 8 + 6

= -1 + 6

= 5

By using PEDMAS rule, 7 + (5 – 9)2 + 3(16 ÷ 8) is  5.

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The solution of equation, 7 + (5 – 9)2 + 3(16 ÷ 8) is,

⇒ 29

Since, We knw that,

PEMDAS stands for P- Parentheses, E- Exponents, D- Division, M- Multiplication, A- Addition, and S- Subtraction.

We have to given that,

Expression is,

7 + (5 - 9)² + 3(16 ÷ 8)

Now, Simplify By using PEDMAS rule,

= 7 + (5 - 9)² + 3(16 ÷ 8)

= 7 + (-4)² + 3(2)

= 7 + 16 + 6

= 23 + 6

= 29

Thus, By using PEDMAS rule, 7 + (5 – 9)2 + 3(16 ÷ 8) is, 29

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Answer:

Step-by-step explanation:

Hello, let's say that the price was P, a real number.

After 20% discount it become P - 20% * P = P* (1-20%) = P * (1 - 0.2)

= P * 0.8

And then we take 15% for the VAT, the new price become P * 0.8 * ( 1 + 15%)

= P * 0.8 * 1.15

And this is equal to 22080, so

P * 0.8 * 1.15 = 22080

and the amount of the VAT is P *0.8 * 0.15

[tex]=\dfrac{22080}{1.15}*0.15=2880[/tex]

Hope this helps.

Thank you.

Answer:

The square root of 2, or the (1/2)th power of 2, written in mathematics as √2 or 2​1⁄2, is the positive algebraic number that, when multiplied by itself, equals the number 2. Technically, it is called the principal square root of 2, to distinguish it from the negative number with the same property

Step-by-step explanation:

Answer:

6 meters per second upwards

Step-by-step explanation:

Hello!

To find velocity you divide the distance by the time it took to travel then you add your direction to it

The elevator went 210 m upwards in 35 seconds so we divide these numbers

210 / 35 = 6 meters per second upwards

The answer is 6 meters per second upwards

Hope this Helps!

Answer:

The best estimated value of the expression is negative 3

Step-by-step explanation:

What is the best estimate for the value of the expression? (StartFraction 34 over 8 EndFraction minus StartFraction 16 over 3 EndFraction) minus StartFraction 14 over 9 EndFraction

Solution

(34 / 8) - (16 / 3) - (14 / 9)

= 34/8 - 16/3 - 14/9

Find the sum

= 306 - 384 - 112 / 72

= -190 / 72

= -2 46 / 72

= -2 23 / 36

= -2.6389

Approximately -3

The best estimated value of the expression is negative 3

Answer:

The answer is -2 1/2,

Step-by-step explanation:

Answer:

  7/6

Step-by-step explanation:

You have correctly graphed the line, so you know that the rate of change is ...

  ∆d/∆t = 7/6

d changes by 7/6 units for each unit change in t.

Answer:

  B.  8x + 9y = 6

Step-by-step explanation:

You can eliminate answer choices A and C because their leading coefficient is negative. In standard form, the leading coefficient is positive.

For the remaining two equations, you can check to see if the given points are on the line

B: for point (-6, 6), we want 8(-6) +9(6) = 6 . . . true

  for point (3, -2), we want 8(3) +9(-2) = 6 . . . . true

The appropriate equation is 8x +9y = 6.

D: (we don't need to check to know it won't work after the above)

__

The equation in standard form, can be written from ...

  (Δy)(x -a) = (Δx)(y -b) . . . . . for some point (a, b)

The values of Δx and Δy are the differences between corresponding coordinates.

  Δy = 6 -(-2) = 8

  Δx = -6 -3 = -9

For point (-6, 6), the above equation becomes ...

  8(x +6) = -9(y -6)

  8x +48 = -9y +54 . . . . eliminate parentheses

  8x +9y = 6 . . . . . . . . . . add 9y-48

Answer:

30 gallons of tea

Step-by-step explanation:

We are looking at the average of cups of tea per minute but we are given the time frame of lunch in hours, so first, we have to convert the hours to minutes:

There are 60 minutes in 1 hour and lunch is 2 hours long.  So, multiply 60 by 2 to get 120 minutes total.

Next, we have to find out the number of cups of tea poured during the lunch.  We have been told already that an average of 4 cups of tea are poured a minute.

Therefore, multiply 4 by the total number of minutes for lunch.  You will multiply 4 by 20 to get 480 cups of tea poured in total during the catered lunch.

Finally, we have to see how many gallons of tea the caterer should bring.  We should know that there are 16 cups in one gallon.

That means we have to divide the total number of cups poured by 16.  Divide 480 by 16 to get 30 gallons of tea that the caterer should bring.

Answer:

The manatee was swimming very passively when all of a sudden it saw a  parrot fish! The parrot fish was considered incredibly rare where the manatee lived and was very playful with manatees. The manatee chased the parrot fish but as if playing tag, the parrot fish agilely swam farther and farther away. At this point the manatee and parrot had been playing "tag" for 300 seconds and were 1000 feet away from the dock where the manatee lived. Eventually when the manatee and parrot fish hit 400 seconds, the manatee became exhausted and decided to head back to the dock but all of a sudden the parrot fish slapped it with its fins! Unable to take the provocation the manatee became filled with vigor once again and started playing again but at the 500 mark it truly became exhausted and no longer could play regardless of what the parrot fish did and headed back to the dock. It took 150 seconds to get back to the dock and it had been away from the dock for 650 seconds.

Answer:

6

Step-by-step explanation:

To calculate x+10, we first need to find x. To do this, we can use the first equation.

We are given the equation:

[tex]x^2-8x=48[/tex]

To solve for x, turn one side of the equation into 0 and solve. Therefore:

[tex]x^2-8x=48\\x^2-8x-48=0\\(x-12)(x+4)=0\\x=-4, 12[/tex]

So, the possible values for x are -4 and 12.

However, we are also told that x<0. In other words, x must be negative. Thus, we can remove 12. That leaves us with: x=-4.

So:

[tex]x+10\\(-4)+10\\=6[/tex]

Answer:

[tex]a_{n}[/tex] = - 2[tex]a_{n-1}[/tex]

Step-by-step explanation:

A geometric recursive formula has the form

[tex]a_{n}[/tex] = r[tex]a_{n-1}[/tex]

where r is the common ratio

Here r = - 14 ÷ 7 = - 2, thus

[tex]a_{n}[/tex] = - 2[tex]a_{n-1}[/tex] with a₁ = 7

Answer:

  2n+2 ways to win

Step-by-step explanation:

You generalize by observing patterns in the way you solve the smaller problems.

The number of winning moves is 2n+2: the total of the number of diagonals, columns, and rows.

For an n×n board, there are 2 full-length diagonals, n columns, and n rows, hence 2+n+n = 2n+2 ways to win.

Answer:1&3

Step-by-step explanation:

Answer:

126

Step-by-step explanation:

Let x be the missing length

The triangles are similar:

● UE/140 = 45/x

From the graph we deduce that:

● UE = 140 - 90 = 50

Replace UE by its value

● 50/ 140 = 45/x

Switch x and 50

● x / 140 = 45/50

45/50 is 9/10 wich is 0.9

● x/140 = 0.9

Multiply 0.9 by 140

● x = 140 × 0.9

● x = 126

Answer:

I think its c 126

Step-by-step explanation:

Answer:

Hey there!

The angle is 24 degrees.

The angle complementary to the 66 degrees is 24 degrees, and the unknown angle is also 24 degrees because these  are alternate interior angles.

Let me know if this helps :)

Answer: 4.5 oz/25.5 g = 1 oz/X g  

Step-by-step explanation: Crossed multiplies to solve for X.

For each value of y, the number of value of x must be one. Then the correct options is D.

The complete question is attached below.

The relation function is given as, for every independent value, there is a dependent value.

Let the function be y = f(x).

For each value of x, the number of value of y may one or two.

But for each value of y, the number of value of x must be one.

Then the correct options is D.

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Answer:

B.22

Step-by-step explanation:

4+4+7+7=22

Answer:

Domain : [-2, 6], {x | -2 ≤ x ≤ 6}

Range : [-6, 2], {y | -6 ≤ y ≤ 2 }

Step-by-step explanation:

Domain of a function is defined by the x-values on the graph of the function.

Similarly, y-values define the Range of the function.

From the graph of a circle,

Diameter of the circle along x-axis (horizontally) has the ends at x = -2 and x = 6

Therefore, domain of the circle will be [-2, 6], {x | -2 ≤ x ≤ 6}

Extreme ends of the diameter of the circle along y-axis are at y = 2 and y = -6

Therefore, range of the circle will be [-6, 2], {y | -6 ≤ y ≤ 2 }

Answer:

The series is given as follows;

[tex]-\dfrac{161}{8} , \ -\dfrac{59}{4} , \ -\dfrac{75}{8}, \ -4, \ \dfrac{22}{16} ......[/tex]

Step-by-step explanation:

Assuming the series is an arithmetic progression, (AP), series, we have

The nth term of the desired series = a + (n - 1)×d

Where;

a = The first term

n = The position of the term in the series

d = The common difference

Given that the 5th term = 22/16 and the 4th term = -4, we have;

d = The difference between consecutive terms = Difference between the 5th term and the 4th term

∴ d = 22/16 - (-4) = 43/8 = 5.375

22/16 = a + (5 - 1)×5.375

∴ a = 22/16 - 4×5.375 = -20.625

The series is therefore;

[tex]-\dfrac{161}{8} , \ -\dfrac{59}{4} , \ -\dfrac{75}{8}, \ -4, \ \dfrac{22}{16} ......[/tex]

Answer:

358.125

Step-by-step explanation:

Answer:

358 3/24

Step-by-step explanation:  

Answer:

JK = 6.86

Step-by-step explanation:

The parameters given are;

LJ = 14

JM = 48

LM = 50

[tex]tan(\angle JML )= \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length} = \dfrac{LK}{JM} = \dfrac{14}{48} = \dfrac{7}{24}[/tex]

[tex]tan \left( \dfrac{7}{24} \right)= 16.26 ^{\circ }[/tex]

∠JML = 16.26°

Given that ∠JML is bisected by KM, we apply the angle bisector theorem which states that a ray that bisects an interior angle of a triangle bisects the opposite (bisected angle facing side) in the proportion of the ration of the other two sides of the triangle.

From the angle bisector theorem, we have;

LM/JM = LK/JK

50/48 = LK/JK................(1)

LK + KJ = 14.....................(2)

From equation (1), we have;

LK = 25/24×JK

25/24×KJ + JK = 14

JK×(25/24 + 1) = 14

JK × 49/24 = 14

JK = 14×24/49 = 48/7. = 6.86.

JK = 6.86

Answer:

13x + 7 = 5x - 20

Step-by-step explanation:

SOLVE for X

13x + 7 = 5x - 20

-------------------------

-5x                   -7  

------------------------

8x=-27

x= -3.375 or -27/8

Answer:

x = -27/8

Step-by-step explanation:

combine the x terms.  To do this, subtract 5x from both sides.  We get:

8x + 7 = -20.  

Next, subtract 7 from both sides, obtaining:

8x = -27, or x = -27/8

Answer:

f₁(x) = -3x + 2

f₂(x) = x - 4

f₃(x) = x + 8

f₄(x) = -2x - 6

f₅(x) = -3x

Step-by-step explanation:

1). Since function f₁ (blue line) passes through a point (0, 2) and (-2, 8)

Let the equation of the blue line is,

y = mx + b

Since slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{8-2}{-2-0}[/tex]

m = -3

Y-intercept 'b' = 2

Therefore, equation of the line will be,

y = -3x + 2

Linear function representing the line will be,

f₁(x) = -3x + 2

2). Let the equation of the red line passing through (0, -4) and (2, -2) is,

y = mx + b

Slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{-4+2}{0-2}[/tex]

m = 1

y-intercept 'b' = -4

Therefore, the linear function will be,

f₂(x) = x - 4

3). Let the equation of the green line passing through (-6, 2) and (-2, 6) is,

y = mx + b

Slope of the line 'm' = [tex]\frac{6-2}{-2+6}[/tex]

m = 1

y-intercept 'b' = 8

Therefore, linear function will be,

f₃(x) = x + 8

4). Let the equation of the yellow line passing through (-6, 6) and (-4, 2) is,

y = mx + b

Slope of the line = [tex]\frac{6-2}{-6+4}[/tex]

m = -2

y-intercept of the line 'b' = -6

Therefore, function representing the line will be,

f₄(x) = -2x - 6

5). Let the equation of the pink line is passing through (0, 0) and (-2, 6) is,

y = mx + b

Since the line is passing through origin, y-intercept 'b' = 0

Slope of the line = [tex]\frac{6-0}{-2-0}[/tex]

m = -3

Therefore, equation of the linear function will be,

f₅(x) = -3x

Answer:

75 pounds

Step-by-step explanation:

(x) + (x) + (x+20) = 185

3x + 20 = 185

3x = 165

x = 55

Large dog = 55 + 20 = 75

Answer:

Step-by-step explanation:

Domain of a function represents the set of x-values (input values) and y-values (output values) of the function represent the Range of the function.

Given function is,

[tex]y=-\frac{2}{3}x+7[/tex]

If Domain (input values) of this function is,

{-12, -6, 3, 15}

Table for the input-output values of this function,

x        -6         3        15       -12

y        11         5         -3        15

Answer:

Step-by-step explanation:

Answer:

1. GH

2. a

Step-by-step explanation:

Perpendicular: When 2 lines meet at 90 degrees

1. It is line segment GH because AB and GH meet at a 90 degree angle (since there is a box at angle GHF indicating that it is 90 degrees)

2. It has to be a units because it is a rectangle where the top and bottom are congruent and the sides are too

This is a rectangle since AB and CD are parallel and GH can be a transversal line, according to same side interior angles theorem EGH is a also 90 degrees. That means FEG is 90 degrees too because then the quadrilateral will add up to 360 degrees

Answer:

NOT IN MY HOUSE SUNNY

Step-by-step explanation:

Answer:

The answer to your question is given below.

Step-by-step explanation:

1. f(x) = 5x + 1

x = – 5

f(x) = 5x + 1

f(–5) = 5(–5) + 1

f(–5) = –25 + 1

f(–5) = –24

2. f(x) = 5x + 1

x = – 1

f(x) = 5x + 1

f(–1) = 5(–1) + 1

f(–1) = –5 + 1

f(–1) = – 4

3. f(x) = 5x + 1

x = 1

f(x) = 5x + 1

f(1) = 5(1) + 1

f(1) = 5 + 1

f(1) = 6

4. f(x) = 5x + 1

x = 2

f(x) = 5x + 1

f(2) = 5(2) + 1

f(2) = 10 + 1

f(2) = 11

5. f(x) = 5x + 1

x = 2

f(x) = 5x + 1

f(3) = 5(3) + 1

f(3) = 15 + 1

f(3) = 16

Summary

x >>>>>>>> f(x)

–5 >>>>>> – 24

–1 >>>>>> – 4

1 >>>>>>>> 6

2 >>>>>>> 11

3 >>>>>>> 16